How do you add noise to an FM signal?

This is Frequency modulation where

where

Question:

I have been able to modulate the message signal m(t) and demodulate it suing this code:

fc = 1000;
Ac = 5;
t0 = 0.2;
ts = 0.00000001;
fs = 1/ts;
t=[0:ts:t0];

m = 10*t.*(t>=0 & t<=0.1)+(2-10*t).*(t>0.1 & t<=0.2)+0.*(t>0.2);

u = Ac*modulate(m,fc,fs,'fm');      %% modulate the message signal

y = demod(u,fc,fs,'fm');            %% demodulate the message signal 
y = y/(6.275*10^-5);                %% scale the demodulated signal

figure(6)
subplot(2,1,1)
plot(t,m(1:length(t)));
title('Original Message signal m(t)')
xlabel('Time (s)')
ylabel('Amplitude')

subplot(2,1,2)
plot(t,y);
title('Demodulated Message Signal')
xlabel('Time (s)')
ylabel('Amplitude')

I now need to add noise to the signal according to the above formula of y(t) = u(t) + n(t)

where n(t) = nc(t).cos(2\pi fc.t) - ns(t).sin(2\pi fc.t)

How do I add this noise to u(t) using rand or randn ?

Answer 1

[Hiro Yoshino]

You can check this up:

https://jp.mathworks.com/matlabcentral/answers/80714-how-generating-band-limited-white-noise-with-matlab

Basically you should follow this:

1. white noise
2. apply filter with the cutoffs both ends in the frequency domain

[Jared Joselowitz]

I have tried this but it is not working. The demodulated signal looks nothing like the original message signal. Please help.

[Jared Joselowitz]

I have added the noise however, the demodulated signal is indestinguishable from the orignal message signal:

fc = 1000;

Ac = 5;

kf = 25;

t0 = 0.5;

ts = 0.00000001;

fs = 1/ts;

t=[0:ts:t0];

df = 0.45;

nc = 0.2;

ns = 0.2;

m = 10*t.*(t>=0 & t<=0.1)+(2-10*t).*(t>0.1 & t<=0.2)+0.*(t>0.2);

u = modulate(m,fc,fs,'fm');

n = nc*cos(2*pi*fc*t) - ns*sin(2*pi*fc*t);

y = u + n;

dem = demod(y,fc,fs,'fm'); % demodulate the nosey signal

dem = dem/(8.7275*10^-5); % scale the signal

figure(1)

subplot(2,1,1)

plot(t,m(1:length(t)));

title('Original Message signal m(t)')

xlabel('Time (s)')

ylabel('Amplitude')

subplot(2,1,2)

plot(t,dem);

title('Demodulated Noisy Message Signal')

xlabel('Time (s)')

ylabel('Amplitude')

[Hiro Yoshino]

I guess you should add noise before the command "modulation".

see:

https://jp.mathworks.com/help/signal/ref/modulate.html

it says demod works for the signal created by modulation.

Also this can be a help for you

https://jp.mathworks.com/help/comm/ug/fm-modulate-and-demodulate-a-sinusoidal-signal.html?s_tid=srchtitle#responsive_offcanvas

Answer 2

[Manuel A. Vázquez López]

Long time but...did you get to solve this? I'm facing a similar problem. I'm adding some Gaussian noise with standard deviation 1e-2, but that has a huge impact on the demodulated signal (and I was assuming FM should be fairly resilient to it).